wedge Files

Wedge, a C++ library for symbolic computations in differential geometry. Mainly based on GiNaC, also relying on CoCoALib for polynomial computations. 

The essential functionality of Wedge is described in the paper http://arxiv.org/abs/0804.3193. If you use Wedge in your research, please quote that paper.

Here is a list of the current features of Wedge:
- Vector and affine spaces: determine a basis from a list of generators, and similar computations.
- Manifolds and differential forms: exterior derivative; wedge product; Lie derivatives.
- Lie groups: the general linear group; subgroups determined by the choice of a subalgebra; abstract Lie groups defined in abbreviated form, e.g. writing (0,0,12) for the Heisenberg group, characterized by the existence of a basis of left-invariant one-forms e1,e2,e3 such that de3=e1 ^ e2 and e1,e2 are closed.
- Riemannian metrics and G-structures, defined on a Lie group or a coordinate patch of a generic manifold, and represented by an orthonormal basis of 1-forms (adapted frame); spinors, Clifford multiplication.
- Connections: the Levi-Civita connection; curvature; covariant derivatives; define connections on generic manifolds and impose conditions on the Christoffel symbols, e.g. to obtain curvature conditions.
- Riemannian submersions.
- Explicit Lie algebra representations; representations induced on tensor products and exterior algebras over a representation.
- LaTeX output.

Known to work with:
Ubuntu Linux 13.04 64bit with gcc 4.7.3, CoCoALib 0.9953